9514 1404 393
Answer:
y = x² -8x +13
Step-by-step explanation:
Put the roots in the intercept form and multiply it out. For roots p and q, the quadratic is ...
y = (x -p)·(x -q)
y = (x -(4+√3)) · (x -(4 -√3))
y = ((x -4) -√3) · ((x -4) +√3) = (x -4)² -(√3)² . . . . use the special product form
y = x² -8x +16 -3 . . . . use the other special product form
y = x² -8x +13
_____
Comment on the special product
There are a couple of quadratic special products that are useful to remember:
the difference of squares: (a -b)(a +b) = a² -b²
the square of a sum: (a + b)² = a² +2ab +b²
When working with quadratics that have complex or radical conjugate roots, the difference of squares form comes in handy sometimes.
Math can be a lot easier if you learn to recognize and use patterns.
